2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
My workout :
1/4 +1/6 = 5/12 , am stuck after this .
Am stuck !! Pls help !!
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- candygal79
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Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobcandygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour
Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
Now onto the question...
Sally can paint a house in 4 hours, and John can paint the same house in 6 hours
So, according to green rule, Sally paints 1/4 of the house in 1 hour, and John paints 1/6 of the house in 1 hour
COMBINED, the fraction of the house they can paint in 1 hour = 1/4 + 1/6
= 3/12 + 2/12
= 5/12
So, they can paint 5/12 of the house in 1 hour
If they can paint 5/12 of the house in 1 hour, then according to blue rule, they can paint ENTIRE house in 12/5 hours.
12/5 hours = 2 2/5 hours
= 2 hours and a bit
= A
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Alternatively, we can use a bit of logic.candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Notice that John is the SLOWER painter.
John can paint the same house in 6 hours
So, if John were to work with ANOTHER painter who painted at the SAME SPEED, the two identical painters could paint the house half the time.
In other words, they could paint the house in 3 hours.
Since Sally can paint FASTER than John, then John and Sally would be able to paint the house even faster than John and an identical painter.
In other words, John and Sally would be able to paint the house in LESS than 3 hours.
Since only answer choice A is less than 3 hours, the correct answer is A
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Brent
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Hi candygal79,
This question involves 2 people working on a job together, so it's perfect for the Work Formula:
Work = (AxB)/(A+B)
A and B represent the amount of time that it takes each person to paint the house:
A = 4 hours
B = 6 hours
Now plug in...
(4x6)/(4+6) = 24/10 hours
2.4 hours = 2 hours 24 minutes
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question involves 2 people working on a job together, so it's perfect for the Work Formula:
Work = (AxB)/(A+B)
A and B represent the amount of time that it takes each person to paint the house:
A = 4 hours
B = 6 hours
Now plug in...
(4x6)/(4+6) = 24/10 hours
2.4 hours = 2 hours 24 minutes
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Let the house = 12 units.candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Since Sally can paint 12 units in 4 hours, Sally's rate = w/t = 12/4 = 3 units per hour.
Since John can paint 12 units in 6 hours, John's rate = w/t = 12/6 = 2 units per hour.
Combined rate for Sally and John = 3+2 = 5 units per hour.
Time for Sally and John together to paint 12 units = w/r = 12/5 hours = 2 hours, 24 minutes.
The correct answer is A.
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We can solve this question quickly by using a little number sense.candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Sally can paint a house in 4 hours
So, if there were TWO Sallys, they'd be able to paint the house in HALF the time.
In other words, TWO Sallys could paint the house in 2 hours
John can paint the same house in 6 hours
So, if there were TWO Johns, they'd be able to paint the house in HALF the time.
In other words, TWO Johns could paint the house in 3 hours
So, the time it takes Sally and John to paint the house will be BETWEEN 2 hours and 3 hours
This allows us to eliminate B, C, D, and E
Answer: A
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1/4+1/6=5/12 is ok. that means 5/12 th work is done by both in one hour, so complete work will be done in 1/(5/12)=12/5 hours which is equal to 2hours and 24 minutes.candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
My workout :
1/4 +1/6 = 5/12 , am stuck after this .
hope no more confusion left.